Understanding

For natural fish populations,the total number of new additions to the current population in a given

year can be modeled as a function of the existing population size N.We will derive the equation

and explain the effects of harvesting the renewable natural source using a modification of the

existing logistic equation.

One can view the derivation in the pdf folder attached in the MAJOR section of the page.

After which we come to the conclusion that :

Harvesting at rate rk/4 , when the resource stock is at exactly half its carrying capacity k/2 and at

its maximum growth rate rk/4 , allows the population to remain at the level indefinitely since

dx/dt=0.